Imaging systems having ray corrector, and associated methods

ABSTRACT

In an embodiment, a low height imaging system has: one or more optical channels and a detector array, each of the optical channels (a) associated with at least one detector of the array, (b) having one or more optical components and a restrictive ray corrector, and (c) configured to direct steeper incident angle field rays onto the at least one detector.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationsSer. No. 60/609,578, filed on Sep. 14, 2004, entitled Improved MiniatureCamera and Ser. No. 60/697,710, filed on Jul. 8, 2005, entitled RayCorrection Apparatus and Method, both of which applications are herebyincorporated by reference in their entireties. The following U.S.Patents are also incorporated by reference in their entireties: U.S.Pat. No. 5,748,371, entitled Extended Depth of Field Optical Systems toCathey et al., U.S. Pat. No. 6,525,302, entitled Wavefront coding phasecontrast imaging systems to Dowski, Jr., et al., U.S. Pat. No.6,783,733, entitled Combined wavefront coding and amplitude contrastimaging systems to Dowski, Jr., U.S. Pat. No. 6,842,297, entitledWavefront coding optics to Dowski, Jr., U.S. Pat. No. 6,911,638,entitled Wavefront coding zoom lens imaging systems to Dowski, Jr., etal. and U.S. Pat. No. 6,940,649, entitled Wavefront coded imagingsystems to Dowski, Jr.

BACKGROUND

One of the latest trends in imaging devices is miniaturization. Compactimaging systems, such as miniature cameras, have become ubiquitous withthe proliferation of cell phones and other portable handheld deviceswith cameras integrated therein. While the currently available, compactimaging devices are adequate for low resolution image capture forpersonal enjoyment, most provide rather low imaging quality or areundesirably long.

An exemplary imaging system 10 is shown in FIG. 1. System 10 may be, forexample, a miniature camera and is shown to include a group of opticalcomponents 2 (shown here to include two separate refractive elements)and a detector 4. Optical components 2 may be made of an opticalmaterial such as Poly(methyl methacrylate) (PMMA), forming four asphericsurfaces, providing a focal length of 2.6mm and an F# of 2.6 over a 60degree full field of view. Light rays 5 from an object (not shown) aredirected through optical components 2 generally along a Z direction 3,and are imaged onto detector 4. Detector 4 then converts to the imagereceived thereon into a data signal (indicated by a large arrow 7),which is directed to a processor 8. The data signal is processed atsignal processor 8 to result in a final image 9.

Still referring to FIG. 1, optical components 2 of system 10 are locatedsuch that a Z-length (defined as the distance from the first surface ofthe group of optics encountered by an input light ray to the front ofthe detector, and indicated by a horizontal double-headed arrow) isapproximately equal to a length L of detector 4 (indicated by a verticaldouble-headed arrow). In the exemplary imaging system shown in FIG. 1,detector length L is 4.4 mm, while Z-length is set at 4.6 mm.

Continuing to refer to FIG. 1, system 10 (like numerous other shortimaging systems) does not have sufficient degrees of freedom to controlthe variety of optical and mechanical aberrations that are possiblymanifest in the system. That is, since there are so few parts formingthe system (e.g., just a few lenses and their holders, small detector,etc.) and the components are so small in compact applications such as aminiature camera, it is difficult to achieve an ideal design oralignment of the different components and/or to adjust any of thecomponents once assembled. As a result, the resulting images do not havehigh image quality. Further, the potential for introduced aberrationsdue to misalignment of the physical components (e.g., optical components2 and detector 4) of system 10 is significant, thereby requiringincreased precision during manufacture. This requirement increases thecost of system 10, even though the image quality of the resulting systemis relatively poor.

Additionally, in prior art imaging system 10, the angles of rays at theedge of detector 4 may be shallow. That is, an angle θ of the chief ray(which is the light ray passing through the center of the aperturedefined by optical components 2) at the edge of the detector may be upto approximately 30 degrees from the normal of the detector. Since theintensity of light captured at the detector is a function of the angleto the detector, the captured light intensity decreases as the chief rayangle increases. Also, large ray angles may lead to light being capturedby the wrong pixel on the detector, thereby causing pixel cross-talk.Therefore, as images formed with practical complementarymetal-oxide-semiconductor (CMOS), charge-coupled device (CCD), andinfrared (IR) detectors are degraded when the incident light rays arefar from the normal of the detector, large chief ray angles areundesirable. As the Z-length of the system is additionally shortened inan effort to further miniaturize the system, these ray angle problemsare exacerbated and increasingly lead to reduced image quality.

SUMMARY OF THE INVENTION

In an embodiment, a low height imaging system has: one or more opticalchannels and a detector array, each of the optical channels (a)associated with at least one detector of the array, (b) having one ormore optical components and a restrictive ray corrector, and (c)configured to direct steeper incident angle field rays onto the at leastone detector.

In an embodiment, a low height imaging system has: a detector array; anda GRIN lens having a surface with wavefront coding and configured todirect steeper incident angle field rays onto a plurality of detectorsof the detector array.

In an embodiment, a low height imaging system has: a plurality ofoptical channels and a detector array, each of the optical channels (a)associated with at least one detector of the array and (b) having anaspheric GRIN lens.

In an embodiment, a method forms a lens with wavefront coding,including: positioning a lens in a mold; and curing material onto asurface of the lens to form an aspheric surface of the lens withwavefront coding.

In an embodiment, a low height imaging system has: a block of opticallytransmissive material having an entrance aperture, an exit aperture andat least one internally reflective surface, wherein a wavefronttransmitted through the entrance aperture reflects off of the reflectivesurface and exits the exit aperture with wavefront coding.

In an embodiment, a low height imaging system has: a plurality ofoptical channels and a detector array, each of the optical channelsassociated with at least one detector of the array and having anaspheric restrictive ray corrector, wherein the aspheric restrictive raycorrector preferentially directs color towards particular detectors ofthe detector array.

In an embodiment, a photon compensating optical system has: at least oneoptical element and an aspheric surface, wherein a non-constant MTF ofthe system compensates for a range between the object and the opticalelement.

In an embodiment, a restrictive ray corrector has: an optical elementconfigured for placement adjacent to, or coupling to, a detector array,the optical element forming at least one surface such that field rayswithin an optical imaging system are directed towards the detector arraywith an angle of incidence that is closer to a surface normal of thedetector array as compared to angle of incidence of field rays incidenton the detector array without the optical element.

In an embodiment, a low height imaging system has: a first wafercomprising a plurality of detectors; and a second wafer including aplurality of aspheric optical components such that MTF of the imagingsystem has no zeros within a passband of a detectors; the first andsecond wafer being stacked to form a low height imaging system with aplurality of optical channels, each of the optical channels having atleast one optical component and at least one detector.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic illustration of a prior art imaging system.

FIG. 2 is a diagrammatic illustration of a low height imaging system,shown here to illustrate one configuration for chief ray correction.

FIG. 3 is a diagrammatic illustration of a low height imaging system,shown here to illustrate a second configuration for chief raycorrection.

FIG. 4 is a diagrammatic illustration of a short imaging system inaccordance with the present disclosure, including a GRIN lens withWavefront Coding.

FIG. 5 is a diagrammatic illustration of the ray pattern over one halfof a 60 degree field of view incident on a GRIN lens without WavefrontCoding.

FIGS. 6-8 are graphical plots of the calculated ray intercepts for theGRIN lens at one wavelength over the field of view for a variety ofincident angles.

FIG. 9 is a series of graphical plots of the calculated monochromaticmodulation transfer functions (MTFs) for the GRIN lens as a function offield angle.

FIG. 10 is a series of spot diagrams as a function of field angle andobject position for the GRIN lens.

FIGS. 11-16 are illustrations corresponding to FIGS. 5-10 but for a GRINlens modified for use with Wavefront Coding.

FIGS. 17 and 18 are graphical plots of the on-axis exit pupils for thesystems illustrated in FIGS. 5-10 and FIGS. 11-16, respectively.

FIGS. 19-21 and 22-24 are sampled images of a point object as a functionof the field angle for the systems illustrated in FIGS. 5-10 and FIGS.11-16, respectively.

FIG. 25 is a graphical plot of the MTFs of an imaging system includingthe GRIN lens modified for use with Wavefront Coding, shown here toillustrate the differences in the MTFs before and after the signalprocessing.

FIGS. 26 and 27 are graphical plots of the digital filter used to formimages in FIGS. 22-25 in an image format and a mesh format,respectively.

FIG. 28 is a diagrammatic illustration of a fabrication system for themanufacture of the modified GRIN lens.

FIG. 29 is a diagrammatic illustration of a measurement system for theevaluation of the modified GRIN lens.

FIG. 30 is a graphical plot of an exemplary thin film spectral filterresponse suitable for use with the modified GRIN lens.

FIG. 31 is a diagrammatic illustration of an imaging system inaccordance with the present disclosure, shown here to illustrate the useof a set of grouped GRIN lenses for increasing the field of view of theimaging system.

FIG. 32 is a diagrammatic illustration of another imaging system inaccordance with the present disclosure for increasing the field of viewof the imaging system, shown here to illustrate the use of analternative correction and steering optics.

FIG. 33 is a diagrammatic illustration of an alternative imaging systemin accordance with the present disclosure, shown here to illustrate theuse of reflective, miniature optics for further reducing the overalllength of the imaging system.

FIG. 34 is a ray diagram of light rays incident on an individual lensletforming a portion of a lenslet array.

FIG. 35 is a diagrammatic illustration, in elevation, of a lenslet arrayformed from a plurality of individual lenslets, as shown in FIG. 34,which lenslet array is suitable for use in place of the grouped GRINlenses shown in FIGS. 31 and 32.

FIG. 36 is a ray diagram of light rays transmitted through a foldedoptics configuration suitable for use in the imaging systems shown inFIGS. 31 and 32.

FIG. 37 is a diagrammatic illustration, in elevation, of a general arrayrepresentation of a miniature optical system including several imagingsystems, such as those shown in FIGS. 31 and 32.

FIG. 38 is a diagrammatic illustration, in partial cross section, of adetector array subsystem in accordance with the present disclosure.

FIG. 39 is a diagrammatic illustration, in partial cross section, of aportion of a prior art detector array subsystem, shown here toillustrate light rays traveling through a lenslet array onto a substrateincluding a detector array without any ray correction.

FIGS. 40 and 41 are diagrammatic illustrations, in partial crosssection, of a portion of the detector array subsystem in accordance withthe present disclosure, and are shown here to illustrate light raystraveling through the lenslet array and onto the detector array with thecorrective element, in accordance with the present disclosure, indifferent locations with respect to the lenslet array.

FIG. 42 is a diagrammatic illustration, in partial cross section, of aray correction system in accordance with the present disclosure,including a plurality of corrective elements in a stack over the lensletarray.

FIG. 43 is a diagrammatic illustration, in partial cross sectional view,of another embodiment of a ray correction system, in accordance with thepresent disclosure, including a plurality of corrective elements as wellas a color filter array.

FIGS. 44-46 are diagrammatic illustrations, in cross section, ofexamples of corrective elements suitable for use as corrective elementsin the ray correction system of the present disclosure.

FIG. 47 is a diagrammatic, top view illustration of a portion of a waferwith an array of corrective elements disposed over an array of detectorelements (not visible), shown here to illustrate an example of apossible shape of the corrective elements.

FIG. 48 is a diagrammatic illustration, in partial cross sectional view,of a light ray traveling through an exemplary corrective element, shownhere to illustrate a possible type of ray correction provided by acorrective element in the ray correction system of the presentdisclosure.

FIG. 49 is a diagrammatic illustration, in partial cross section, of alight ray traveling through an enhanced corrective element of thepresent disclosure, shown here to illustrate some of the possiblemodifications that may be made to the corrective element itself in orderto enhance the ray correction.

FIGS. 50-54 are diagrammatic illustrations, in partial cross section, oflight rays traveling through additional embodiments of a ray correctionsystem of the present disclosure, shown here to illustrate possiblevariations for customizing the ray correction characteristics of the raycorrection elements.

FIGS. 55 and 56 are diagrammatic illustrations of a front view and aside view of a color separation function that may be provided by a pairof cascaded corrective elements, in accordance with the presentdisclosure.

FIGS. 57-59 are diagrammatic illustrations of cross-sectional, top viewsof the color separation function illustrated in FIGS. 55 and 56, shownhere to illustrate the separation of color into different spatialregions as a result of passing through the cascaded corrective elements.

FIG. 60 is a diagrammatic illustration of a Bayer color filter arraypattern.

FIG. 61 is a diagrammatic illustration of spatial color separationachieved using the cascaded corrective elements used to produce thecolor separation shown in FIGS. 55-59, shown here to illustrate that thespatial color separation function may be customized such that theresulting color separation corresponds to the color distribution of theBayer filter array pattern as shown in FIG. 60.

FIG. 62 is a diagrammatic illustration, in cross sectional view, of aprism for use in spatially dispersing illumination by wavelength, whichis suitable for use in the spatial color separation function inaccordance with the present disclosure.

FIG. 63 is a diagrammatic illustration, in partial cross section, of atwo-level, binary diffractive structure for use in spatially dispersingillumination by wavelength, which is also suitable for use in thespatial color separation function in accordance with the presentdisclosure.

FIG. 64 is a diagrammatic illustration, in partial cross section, of ablazed diffractive structure, which is also suited for the spatial colorseparation of the present disclosure.

FIG. 65 is a graphical plot of two exemplary focal length versus pupillocation curves for two different Wavefront Coded systems, shown here tocompare the characteristics of a cubic phase system and a constantsignal-to-noise ratio (SNR) system.

FIG. 66 is a graphical plot of the ambiguity function (AF) for aone-dimensional, linearly changing focal length system, and FIG. 67 is agraphical plot of the response versus normalized misfocus at a crosssection of the AF of FIG. 66 at a normalized spatial frequency line of0.175.

FIG. 68 is a graphical plot of the ambiguity function (AF) for aone-dimensional, exponentially changing focal length system, and FIG. 69is a graphical plot of the response versus normalized misfocus at across section of the AF of FIG. 68 at a normalized spatial frequencyline of 0.175.

FIG. 70 is a graphical plot of the ambiguity function (AF) for atraditional imaging system with no Wavefront Coding.

FIG. 71 is a graphical plot of the response versus normalized misfocusat a cross section of the AF of FIG. 70 at a normalized spatialfrequency line of 0.175.

FIG. 72 is a flowchart illustrating a method for applying WavefrontCoding to optical systems.

It is noted that, for purposes of illustrative clarity, certain elementsin the drawings may not be drawn to scale.

DETAILED DESCRIPTION

Optical systems and devices are now described which increase imagequality even though they have a short z-length, or equivalently lowheight, with respect to the size of the detector. “Short” or “lowheight” is generally defined as a Z-length (from the first surface ofthe optics to the front of the detector) that is less than twice theeffective focal length of the optical system.

These systems and devices may provide other advantages, for example theymay provide: relaxed tolerances (to reduce costs) of the optics,mechanics, and digital detector while still achieving high imagequality; for use of modified off-the-shelf short volume optics for highquality imaging; for use of customized short volume optics for highquality imaging; for use of customized short volume optics withreflections for high quality imaging; for use of groups of short volumeoptics to form high quality images; for use design of specialized exitpupils for specialized imaging systems such that detection probability,or image signal-to-noise ratio (SNR), is a constant over a range ofobject distances. These systems can also offer an increase in systemlight sensitivity.

While the optical systems and devices of the present disclosure mayinclude refractive and/or diffractive elements therein, the main purposeof these additional elements is not to focus the incident light onto aparticular spot on, for example, a detector, but to steer the incidentlight, without necessarily focusing, toward a desired location whileachieving the desired incident angle at the detector. That is, theteachings herein provided are directed to “channeling” the light inparticular ways or, in other words, steering the light along one or moredesired “optical channels” so as to provide advantages such as increasedlight intensity at detectors, customizable chromatic separations, andreduced system size.

One known attempt to solve the problem of large ray angles at thedetector in short imaging systems is shown in FIG. 2. FIG. 2 shows anexemplary low height imaging system 20 that includes optical components12 and detector 14 generally arranged along a Z direction 13, similar tooptical components 2 and detector 4 arranged along Z direction 3 ofimaging system 10, FIG. 1. Low height imaging system 20 also includes arefractive restrictive ray corrector lens 22 located at or near detector14. Refractive restrictive ray corrector lens 22 causes certain rayangles to be steeper at detector 14 than the ray angles would be withoutrefractive restrictive ray corrector lens 22. The maximum chief rayangle for system 20 of FIG. 2 may be decreased by a factor of 6, ascompared to the maximum chief ray angle of system 10, to 5 degrees withrefractive restrictive ray corrector lens 22 placed before the detector.This resulting chief ray angle of 5 degrees is considered to be smalland within the good quality operational region of most practicaldetectors.

Continuing to refer to FIG. 2, one potential drawback to system 20 isthat, since refractive restrictive ray corrector lens 22 is refractive,it has a significant thickness. The thickness of refractive restrictiveray corrector lens 22 is generally about 1 mm, which is a thicknesslarge enough to cause the ray angle to decrease but also potentiallyadds other aberrations to the wavefront of light rays 15 before detector14.

FIG. 3 shows an alternative low height imaging system 30 that includesoptical components 12 and detector 14 similar to optical components 2and detector 4 of imaging system 10, FIG. 1. Low height imaging system30 also includes a diffractive restrictive ray corrector 32 (e.g., aFresnel lens) that functions in a similar manner to refractiverestrictive ray corrector lens 32 of system 20. Diffractive restrictiveray corrector 32 has a greatly reduced thickness as compared torefractive restrictive ray corrector lens 22 while providing the samefunction. While the maximum ray angles at the detector are still about 5degrees, the small thickness of diffractive restrictive ray corrector 32means that virtually no additional aberrations are introduced to thewavefront of light rays 15 before they are incident on detector 14. Inpractice, diffractive restrictive ray corrector 32 may be less than 1/10mm depending on the material used, the range of wavelengths used, andthe spacing of diffractive zones. FIG. 3 also shows light ray groups16(1), 16(2) and 16(3) to illustrate how optical channels are associatedwith light passing through optical component 12 to ray corrector 32,thereby steering the light into respective detectors of detector array14.

One way of removing the need to correct ray angles at or near thedetector is to make the imaging system telecentric at the image. Animage side telecentric imaging system has chief ray angles that areessentially parallel to the optical axis. The ray angles at the detectorfor telecentric lenses can then only be related to the marginal rayangles (i.e., those rays from the edge of the lens to the image plane),which is related to the speed or F/# of the lens. No additional rayangle is introduced due to the distance of the image point from theoptical axis. In practice, the imaging system only has to havetelecentric properties; it does not have to be strictly telecentric.

Short telecentric refractive optics can be constructed where the imageof the aperture, as seen from the detector side of the lens, is at orclose to infinity. For the image of the aperture to appear nearinfinity, the aperture should be in front of the last group of optics,with the distance between the aperture and the group being the effectivefocal length of the last group. For a two element imaging system, suchas shown in FIG. 1, the distance from the aperture to the second elementhas to be approximately the focal length of the second element for thesystem to be close to telecentric. However, the need to increase thedistance between the two elements works against the goal of making veryshort imaging systems. When designing increasingly shorter refractiveimaging systems, at some point it is not possible to make the systemstelecentric and also meet a length constraint.

For example, the following describes an improved miniature camera.Similar techniques may be employed within cell phone cameras, digitalcameras, endoscopes, automotive imaging systems, toys, infra-red (IR)imaging systems, biometric imaging systems and security systems.

In certain embodiments herein, telecentric imaging is provided throughgradient index (GRIN) optics. GRIN optics have index of refractionchanges that in general are a function of position within the optic.GRIN optics may have a spatially varying index of refraction given byn(r, z)=Σa _(i) r ^(i) +b _(i) z ^(i)where n(r, z) is the index of refraction in the radial (r) and axial (z)directions. The sum is over the parameter i. Other variations in theform of the index of refraction are possible. Some variations includethe index of refraction changing as a function of thickness z along aspherical or lens-shaped contour and dynamically changing indexdistributions. By proper configuration of the GRIN optics, the imagingsystem can be approximately telecentric while also being short.

FIG. 4 shows a short imaging system 100 that includes a modified GRINlens 104. Modified GRIN lens 104 (e.g., originally an NSG (Nippon SheetGlass) GRIN lens ILH-0.25) is modified to implement Wavefront Coding andis disposed in front of a detector 102 to achieve a short length, highspeed, and a very wide field of view. Modified GRIN lens 104 has acustomized front surface 106 that includes a specially designedcomponent employing Wavefront Coding. Signal processing of the resultingimage from detector 102 may be utilized to reverse the spatial effectsof the Wavefront Coding and produce a final image. A rear surface 107 ofmodified GRIN lens 104 is positioned nearly adjacent to or in contactwith detector 102. One side of modified GRIN lens 104 includes ablackened exterior surface 108 for absorbing light and for reducingreflections, as well as acting as a field stop. The NSG ILH-0.25 GRINlens, on which modified GRIN lens 104 is based has a focal length off=0.25 mm, F/1, diameter=250 μm, length=400 μm, and a full field of view(FOV) of 60 degrees. Detector 102 may be, for example, a 56×56 pixelCMOS detector with 3.3 μm square pixels. In addition to customized frontsurface 106, the front or the rear surface of modified GRIN lens 104 mayalso be coated with a thin film spectral filter. In short imaging system100, the use of specialized surfaces and gradient index optics resultsin a substantially telecentric optical system with a short total length(Z-length). Telecentric optics help to ensure that the chief ray anglesat the detector surface are steep enough to remain within a practicalrange of input angles for readily available detectors.

The performance of a GRIN lens without Wavefront Coding is shown inFIGS. 5-10. FIG. 5 shows a ray pattern 120 for a plurality of inputlight rays (indicated by a dashed oval 122) over one half of a 60 degreefield of view into a GRIN lens 124. Input light rays enter a frontsurface 125 of GRIN lens 124 and are focused at a rear surface 126 ofGRIN lens 124, which is disposed adjacent to a detector 127. Due to thegradient index configuration of GRIN lens 124, a plurality of ray angles(indicated by a dashed oval 128) at the detector are all small, on theorder of 20 degrees or less. The maximum ray angle at the detector ismainly determined by the speed of this GRIN lens, which is F/1.

FIGS. 6-8 illustrate the ray intercept diagrams for GRIN lens 124 at onewavelength over the field of view. Each pair of plots in FIGS. 6-8correspond to the image point versus pupil point over the GRIN lensaperture at the input surface (shown as front surface 125 in FIG. 5) fordifferent input ray angles; the scale of each of the plots in FIGS. 6-8is from −5 microns to +5 microns. The ray intercept diagrams shown inFIGS. 6-8 indicate that GRIN lens 124 suffers from a large amount offield curvature, spherical aberration, coma, and astigmatism. Theperformance at other wavelengths is similar. These aberrations greatlylimit the imaging performance at all but the on-axis positions.

FIG. 9 shows monochromatic modulation transfer functions (MTFs) for GRINlens of FIG. 5 as a function of field angle. The MTF is seen to dropdrastically for increasing field angles. At the largest field angles,the MTF has zeros near 110 lp/mm. The maximum spatial frequency capturedby the 3.3 micron pixel detector is about 151 lp/mm. The image qualitycaptured by the detector will then greatly depend on the image locationto due the aberrations of field curvature, spherical aberration, coma,and astigmatism.

FIG. 10 shows the spot diagrams for GRIN lens 124 as a function of fieldangle and object position. As can be seen in FIG. 10, the shape and sizeof the spot diagrams vary greatly over field and image plane. Thisvariation again shows that this GRIN lens would, on its own, imagepoorly in a large field of view configuration.

By using Wavefront Coding through specialized types of the opticalsurfaces that form the lens, and signal processing of the resultingimages, the effects of aberrations due to the optics, mechanics,environment, fabrication, and assembly can all be controlled. The signalprocessing increases the degrees of freedom of the overall system thatcan be used to compensate for the relatively small number of degrees offreedom of the physically short imaging system.

Through Wavefront Coding, even off-the-shelf gradient index (GRIN) fast(F/1) lenses can be made to image with high spatial resolution (3.3micron pixels) over a large field of view (60 degree full field ofview). A GRIN lens that has been modified for use with Wavefront Codingis shown in FIG. 11. FIG. 11 shows a ray pattern 130 for a plurality ofinput light rays (indicated by a dashed oval 132) over one half of a 60degree field of view into a modified GRIN lens 134. Input light raysenter a front surface 135 of modified GRIN lens 134 and are focused at arear surface 136 of GRIN lens 134, which is disposed adjacent to adetector 137. Ray angles (indicated by a dashed oval 138) at rearsurface 136 are again small. Detector 137 converts the light signalsreceived thereon into an electrical signal 140, which is directed to asignal processing unit 142. Resulting electrical signal 144 from signalprocessing unit 142 is used to form a final image 146.

Modified GRIN lens 134 differs from GRIN lens 124 of FIG. 5 by theformation of a specialized surface at front surface 135 of modified GRINlens 134. Notice the different shape of the ray bundles at rear surface136 in FIG. 11 compared to the ray bundles at rear surface 126 in FIG.5. The specialized surface formed at front surface 135 of modified GRINlens 134 may implement, for example, a rectangularly separable cubicphase modification. Mathematically, the phase modification is describedas {α(x^3+y^3)}, where α is chosen to give a peak-to-valley optical pathdifference (OPD) of up to about 11 wavelengths. This form for thespecialized surface was chosen for use with modified GRIN lens 134 forsimplicity. A variety of other surface forms are also valuable andpossible. A light signal transmitted through modified GRIN lens 134 anddetected at detector 137 is subsequently processed through signalprocessing unit 142. Signal processing unit 142 may, for example,compensate for the phase modifications that were implemented by thespecialized surface. For instance, when the specialized surface isconfigured to be a known Wavefront Coding element, then signalprocessing unit 142 may serve to reverse the spatial effects of thephase modifications introduced by the transmission of light rays throughthe Wavefront Coding.

FIGS. 12-14 show ray intercept curves for modified GRIN lens 134 overfield for a single wavelength; the scale of each of the plots in FIGS.12-14 is from −50 microns to +50 microns. These curves are for theoptics only and do not include the detector or signal processing. Theperformance is similar for other wavelengths. As may be seen in FIGS.12-14, the ray intercept curves are all essentially constant as afunction of field angle. From this result, it would be expected that theresponse from the system as a function of field angle is substantiallyconstant. It is noted that the scale of the ray intercept curves shownin FIGS. 12-14 is 10 times larger than the scale shown in FIGS. 6-8.

MTFs for modified GRIN lens 134 are shown in FIG. 15. These MTFs also donot include the effects of the detector or signal processing. Theoptics-only MTFs are seen to have substantially constant behavior overthe entire field of view. This MTF behavior is very different from thatof GRIN lens 124, as shown in FIG. 9.

Spot diagrams of modified GRIN lens 134 are shown in FIG. 16, whichagain shows optics-only information, without signal processing. The spotdiagrams are seen to be substantially constant over field angle andimage plane. The particular shape of the spot diagrams is determinedmainly by the particular rectangularly separable surface profile usedwith the modified GRIN lens.

The changes that differentiate front surface 135 of modified GRIN lens134 from front surface 125 of GRIN lens 124 are illustrated bycomparison of FIGS. 17 and 18. FIG. 17 represents an on-axis exit pupilprofile 150, in a mesh format, of GRIN lens 124. As may be seen, on-axisexit pupil profile 150 is substantially flat with a slightly curvedprofile. FIG. 18 shows a specialized, on-axis exit pupil profile 155 ofmodified GRIN lens 134. Specialized exit pupil profile 155 is configuredto introduce specific phase modifications to light rays transmittedtherethrough in accordance with the desired Wavefront Coding effect.Front surface 125 and back surface 126 of GRIN lens 124 are consideredsubstantially flat, as shown in FIG. 5. A peak-to-valley OPD isapproximately 2.2 wavelengths for the profile shown in FIG. 17. Incontrast, front surface 135 of modified GRIN lens 134 has a surfaceprofile that implements a rectangularly separable cubic phasemodification. In (x, y) coordinates the form of this surface is{α(x^3+y^3)}, where the constant α is adjusted to achieve a desiredsurface height. The surface height of front surface 135 of modified GRINlens 134 is configured, in the example shown in FIG. 18, such that theon-axis peak-to-valley OPD for the modified GRIN lens is approximately11 wavelengths. Although present on front surface 135 of FIG. 11, thissmall deviation from flat is difficult to see visually.

Images of a point object as a function of field angle after samplingwith the 3.3 micron detector for various field angles, using modifiedGRIN lens 134, are shown in FIGS. 19 through 21. The images of pointobjects, or point spread functions (PSFs), as shown in FIGS. 19 through21 exhibit a characteristic triangular shape for a rectangularlyseparable system, and also exhibit little visual change as a function offield angle. The side length of the PSF in units of pixels is about 10.

As shown in FIG. 11, the images detected at detector 137 are directedthrough signal processing unit 142 for final image formation. PSFs thatresult from processing the images of a point object as imaged throughmodified GRIN lens 134 through signal processing unit 142 are shown inFIGS. 22 through 24. The signal processing used to produce the PSFsshown in FIGS. 22 through 24 is linear digital filtering. A lineardigital filter used in this signal processing is constant over allpositions in the image field. After linear filtering of the sampled PSFsof FIGS. 19 through 21, the filtered PSFs of FIGS. 22 through 24 areseen to be spatially compact and essentially constant over the entirefield. PSFs as a function of object position, for a broad range ofobject positions, although not shown, would be similar to those shown inFIGS. 19 through 21 and 22 through 24 for modified GRIN lens 134.

MTFs of an imaging system using modified GRIN lens 134, employingWavefront Coding before and after signal processing, are shown in FIG.25. As in FIGS. 22-24, the signal processing illustrated in FIG. 25 islinear digital filtering. The MTFs before signal processing are shown asa lower group indicated by a dashed oval 160; the MTFs after signalprocessing are shown in an upper group indicated by a dashed oval 170.The MTFs are representative of the entire field and of a range of objectpositions from 3 to 15 mm. The MTFs also include an ideal pixel MTF froma 3.3 micron detector with 100% fill factor. Referring briefly back toFIG. 9, it may be recalled that an imaging system with a conventionalGRIN lens images with poor quality at even one object distance. As maybe seen from FIG. 25, lower group 160 of the MTFs resulting from themodified system including the modified GRIN lens are seen to besubstantially constant, before signal processing, over all field anglesand over a range of object distances. Signal processing, using the samelinear digital filter applied over all field positions and objectdistances, produces the MTFs shown in upper group 170. It is noted thatMTFs of upper group 170 have substantially the same height as the bestfocused, on-axis MTFs from a conventional GRIN lens (assuming the MTFsfrom the conventional GRIN lens include the pixel MTF of a ideal 3.3micron pixel).

The linear digital filter used to form images in FIGS. 22-24 and theplots of FIG. 25 is represented in FIGS. 26 and 27. FIG. 26 shows arepresentation of the linear digital filter in an image format 500, andFIG. 27 shows a representation of the digital filter in a mesh format550. As may be seen in FIGS. 26 and 27, the linear digital filter isspatially compact, with very few distinct values. Such a digital filteris computationally efficient to implement in hardware processingplatforms. In the example shown in FIGS. 26 and 27, the sum of allvalues of the digital filter is equal to one. A square root of a sum ofsquared values of this filter then gives an approximation to the RMSgain of additive noise (or noise gain) after application of this filter.Thus calculated, the noise gain for this exemplary digital filter is3.2.

An example of a fabrication system 800 that produces a modified GRINlens 802 is shown in FIG. 28, in accord with an embodiment. ModifiedGRIN lens 802 includes a traditional GRIN lens 804 onto which aspecialized phase surface 806 is added. Specialized phase surface 806 isformed on a front surface 808 of traditional GRIN lens 804 using amoldable material such as, but not limited to, a UV-curable material,epoxy, glue, or similar. The shape of specialized phase surface 806 isdetermined by the shape of a machined surface 810 of a pin 812. Asurface 810 of pin 812 is machined to accurately represent the negativeof the surface profile desired for specialized phase surface 806. Theform taken by the moldable material (and, consequently, specializedphase surface 806) is thus determined by the shape of machined surface810 of pin 812. The shape of specialized phase surface 806 may be, forinstance, aspheric. That is, pin 810 is similar to other pins commonlyused in injection molding machines. A measured amount of the moldablematerial is added to machined surface 810 of pin 812, before insertionof traditional GRIN lens 804 into fabrication system 800. A collar 814holds traditional GRIN lens 804, pressing it against pin 812. If aUV-curable material is used as the moldable material, for example, UVcuring light 816 may be introduced through traditional GRIN lens 804from a back surface 818. Back surface 818 of traditional GRIN lens 804may also be coated with a thin film spectral filter 820. If the spectralfilter 820 is added to traditional GRIN lens 804 before the molding ofspecialized phase surface 806, and a UV-curable material is to be usedas the moldable material for the specialized phase surface, thenspectral filter 820 should be configured to pass light at the UV curingwavelengths appropriate to the specific UV-curable material used.Additionally, pin 812 and collar 814 may be coated with a non-stickmaterial, such as TEFLON®, for ready release of modified GRIN lens 802after fabrication.

Referring now to FIG. 29 in conjunction with FIG. 28, a measurementsystem 830 for the evaluation of modified GRIN lenses, such as modifiedGRIN lens 802 of FIG. 28, is described. After pin 812 is removed, butbefore collar 814 is removed, modified GRIN lens 802 is used to form animage 840 of a test object 842, such as a point object, a bar chart, orother suitable object for testing. A microscope objective 844 may beused to focus at a resulting image 840 that forms on rear surface 818 ofmodified GRIN lens 802. Microscope objective 844 cooperates with animaging lens 846 to transfer image 840 onto a remote detector array 848as a transferred image 850. Objective 844 may optionally be, forexample, infinity corrected. In the example shown in FIG. 29, objective844 is assumed to be infinity corrected. By imaging test object 842 ontodetector array 848 while collar 814 is still attached to modified GRINlens 802, quality of transferred image 850 may be iteratively checked.Measurement system 830 may then be used to improve the quality of aparticular modified GRIN lens 802 by indicating whether the specializedphase surface of that particular lens may need to be re-fabricated. Inthis way, measurement system 830 may be used to accelerate the reliablefabrication of modified GRIN lenses. This type of fabrication, testing,and rework method may be used in parallel when groups of GRIN lenses aremade and attached in a group, for example.

An example thin film spectral filter response 870 for a modified GRINlens (e.g., modified GRIN lens 802 of FIG. 28) is shown in FIG. 30. Oneexample of a possible configuration for the thin film spectral filter ofFIG. 30 is described in TABLE 1. TABLE 1 lists the layer material andthickness (i.e., the prescription) of this 13-layer thin film bandpassspectral filter. The imaging passband for this 13-layer filter is about50 nm. The UV passband also has a slightly less than 50 nm widebandwidth. By appropriate design of the various layers within thefilter, imaging bandwidth of spectral filters may be made wide enough tocover the visible band. The effects of the resulting chromaticaberration that would typically result in the traditional GRIN lens canbe removed by design of the Wavefront Coded front surface and signalprocessing of the final images.

TABLE 1 Material Thickness (nm) Air N/A TiO₂ 75.56 SiO₂ 93.57 TiO₂ 34.13SiO₂ 86.48 TiO₂ 58.57 SiO₂ 45.05 TiO₂ 63.34 SiO₂ 113.25 TiO₂ 94.20 SiO₂108.37 TiO₂ 105.07 SiO₂ 145.66 TiO₂ 100.20 Substrate (GRIN lens)

Returning briefly to FIG. 4, the maximum image size of modified GRINlens 104 is, in practice, limited by the range of index of refractionchange within the GRIN lens volume. A change of index of refraction of0.1 is considered common in GRIN lenses. A change of index of 0.3 isconsidered uncommon. Although such larger changes of index of refractionmay become increasingly common in the future, there is a need to balancethe size of the image with the index change currently available.

One system for imaging large objects and for forming increasingly largersize images is shown in FIG. 31. A system 900 includes a group 902 of aplurality of GRIN lenses 904 to form large images. Each of the pluralityof GRIN lenses 904 may be, for example, modified GRIN lens 802 ortraditional GRIN lens 804 of FIG. 28. Each one of plurality of GRINlenses 904 images a small field of regard 906 (i.e., the portion of theobject seen by each GRIN lens) of a large object 908 onto a detector912, which converts the detected optical image into an image data signal917. Image data signal 917 is then processed at a signal processor 918in order to produce a final image 919. As a result, the total image sizeof final image 919 may be much larger than the image size that may beproduced by singly using any one GRIN lens.

In FIG. 31, group 902 of plurality of GRIN lenses 904 is configured suchthat uninterrupted coverage of the entire object 908 may be achieved.Field of regard 906 of each GRIN lens may overlap the fields of regardof any other GRIN lens. System 900 may optionally include a steeringoptics 920 for controlling the field of regard of individual GRINlenses. Steering optics 920 is shown in a refractive configuration inFIG. 31, but other configurations may be used. For example, in adiffractive configuration, steering optics 920 may include one or moreprisms with additional surface variations for optical correction. Suchprisms may also be mounted directly onto the front surface of the groupof GRIN lenses. Steering optics 920 may also be configured to exhibitoptical power and to perform some aberration balancing.

Referring now to FIG. 31 in conjunction with FIG. 4, the WavefrontCoding surface added to the front surface of GRIN lens 104 of FIG. 4 maybe implemented in system 900 of FIG. 31 in, for example, one of threeways: 1) an aspheric surface may be added to a separate refractiveand/or diffractive steering optics, such as a part of steering optics920; 2) an aspheric surface may be directly added to the front surfaceof each one of plurality of GRIN lenses 904 of group 902; or 3) theeffect of customized front surface 106 on the imaging wavefront may beintegrated into the design of each individual GRIN lens of group 902. Itis noted that the third listed method would not require a specializedaspheric surface to be attached or formed at the front or back surfaceof each GRIN lens, as was shown in the fabrication method shown in FIG.28.

Still referring to FIG. 31, an optional correction plate 922 or, simply,free space may be disposed between group 902 of GRIN lenses 904 anddetector 912. For example, if a diffractive or a volume element is usedas correction plate 922, additional aberrations from each GRIN lens maybe mitigated. If free space is used in place of correction plate 922,then the effect of propagation through free space may help smooth thesub-image boundaries between the individual GRIN lenses. Also, theboundaries between GRIN lenses may be blackened so as to act as fieldstops.

Continuing to refer to FIG. 31, since each GRIN lens 904 images adifferent field of regard 906, the individual GRIN lenses, and theircorresponding Wavefront Coding optics, may be specially designed forwide fields of view. Furthermore, the optical property of eachindividual GRIN lens may be customized to image well at particularincident angles at which that GRIN lens receives the light from theobject. In this way, the aberrations inherent in the on-axis viewingGRIN lenses and the off-axis viewing GRIN lenses may be optimallycontrolled. Signal processing 918 for producing final image 919 may alsobe customized for each individual GRIN lens. The signal processingapplied may be, for example, similar to the linear filteringdemonstrated in FIGS. 26 and 27.

Referring now to FIG. 32 in conjunction with FIG. 31, another form ofthe groups of GRIN lens system (employing Wavefront Coding) is shown inFIG. 32. This system shown of FIG. 32 is similar to system 900 of FIG.31 except at the steering optics. Like system 900 of FIG. 31, a system950 includes a group 952 of a plurality of GRIN lenses 954. However,unlike system 900, system 950 includes steering optics 955 configuredsuch that different fields of regard 956 of an object 958 cross at somedistance before detector 912. This arrangement of system 950 helps toreduce some of the requirements placed on a signal processor 964 in thesignal processing of the detected image. The magnification of group 952of GRIN lenses 954 may be negative such that the image is inverted. Itmay be seen in FIG. 31 that portions of object 908 that are farther fromthe optical axis (i.e., the surface normal from the center of detector912) are imaged onto detector 912 closer to the optical axis for asingle GRIN lens. Signal processing 918 is then required to sort thesub-images resulting from each field of regard 906 and to correct themagnification. System 950 of FIG. 32 does not have this magnificationproblem because portions of object 958 that are farther from the opticalaxis are imaged farther from the optical axis in a particular GRIN lens.Therefore, the resulting sub-images do not need to be reversed.

Continuing to refer to FIGS. 31 and 32, signal processing 918 and 964 ofFIGS. 31 and 32, respectively, will still have to remove objectionabledistortions and possible illumination fall off with field angle as wellas remove the blur inherent in images due to Wavefront Coding. It isrecognized that distortion generally increases as the image fieldincreases with GRIN optics as does the illumination decrease. Distortionand illumination correction may be performed before or after the blurremoval. Blur removal may be achieved, for example, with a simple linearfilter as illustrated in FIGS. 26 and 27.

By introducing reflections into miniature optics such as shown in FIG.33 the resulting overall length D of a reflective imaging system 980 maybe decreased. In the example illustrated in FIG. 33, a reflection optic982 includes a first surface 984, which may, for instance, berefractive, diffractive, or include a Fresnel lens. Reflection optic 982also includes additional reflective surfaces 986 and 988 that may beutilized to further modify the wavefront of a light 990 passing throughreflection optic 982. An aperture stop (not shown) may be additionallylocated at or near one of the reflective surfaces. Also, additionalphase modification may be introduced at final surface 992. The materialforming reflection optic 982 may be a GRIN material, a general volumeelement or a homogeneous material. As additional degrees of freedom areintroduced to reflection optic 982 by the presence of reflected surfaces986 and 988, these additional reflective surfaces may offer furthercustomizability to offset the reduction in degrees of freedom whenreplacing a GRIN or general volume material with a homogeneous material.Reflective imaging system 980 may be configured such that the system issubstantially telecentric. That is, the chief ray angles throughreflection optic 982 may be made small such that the resulting incidentangles at detector 994 are small, thereby ensuring that reflectiveimaging system 980 behaves substantially as a telecentric system. Thechief ray angle of light ray transmitted through reflective imagingsystem 980 may be further controlled to reduce the detector intensityloss. Refractive or diffractive surface may also be implemented on othersurfaces of reflection optic 982. If final surface 992 is kept flat,then reflection optic 982 may be mounted directly on the surface ofdetector 994 in a manner similar to modified GRIN lens 104 of FIG. 4.Mounting directly on the detector, or equivalently on the detector coverplate, may greatly decrease the fabrication tolerance of the system.However, if it is impractical to mount imaging system 980 directly ondetector 994, imaging system 980 may also be mounted at some distanceaway from the detector.

FIGS. 34-36 illustrate other configurations of the optical componentsbroadly represented in FIGS. 31 and 32. As earlier discussed, a group ofspecialized GRIN lenses are used as the basis of FIGS. 31 and 32. Ingeneral, there are a many other types of imaging configurations that maybe used in place of the GRIN lens array. That is, similar functionalityto those configurations described in FIGS. 31 and 32 may be achievedusing groups of individual optics. For example, instead of the groupedGRIN lenses 902 and 952 of FIGS. 31 and 32 the grouped optical elementscan be a simple lenslet 1201, through which a bundle of light rays(indicated by a dashed oval 1205) may be transmitted, of FIG. 34 groupedinto a lenslet array 1210 of FIG. 35. The surface form of the array maybe generalized aspheric optics, including Wavefront Coding, such thatthe type of imaging performance achieved by the GRIN lenses, and shownin FIGS. 11-25, may be achieved with the lenslet array. Multiple lensletarrays may also be used such that the arrays are stacked along theoptical axis resulting in increasingly higher quality imaging. Theseparation between imaging arrays along the optical axis can bemaintained through mounting features formed on the arrays or throughseparate array spacers. Array spacers are essentially optical disks withindex of refraction different from that of the array optics or possiblynon-optical disks with holes centered on the optical axes of the arrayoptics.

FIG. 36 shows another optical configuration that can be used in thegrouped lenses 902 and 952 of FIGS. 31 and 32. A folded optics 1220 usedin FIG. 36 acts to fold the path of the optical axis allowing both anadditional optical degree of freedom at the reflection surface and achange in orientation of the detector plane. As a result, a bundle oflight rays 1225 traveling through folded optics 1220 are re-directed ina direction approximately 90-degrees away from the incident direction.Such folded optical configurations can be constructed with a singlephysical component in order to simplify mounting and alignment.

The miniature optics so far described generally have more than a singlelayer of material through which light passes. In FIGS. 31 and 32 threedifferent layers are represented. The first layers (920 and 955) areshown to act as correction and steering optics. Group optics 902 and 952collect the light and transfer toward the detector. Layer 922 acts as afurther correction plate. Each of these layers may be fabricated in anarray fashion such that components important to systems like 900 and 950of FIGS. 31 and 32 are replicated across and along the array. Individualcomponents suitable for systems 900 and 950 may be acquired by cuttingor dicing the needed components from the array. As is well known,electronic sensors, such as CMOS sensors, are fabricated in a arrayfashion on a silicon substrate or wafer. Individual sensors are acquiredfrom the wafer by cutting or dicing.

FIG. 37 shows a general array representation of miniature opticalsystems, of which systems 900 and 950 of FIGS. 31 and 32 are particularexamples. FIG. 37 shows a system 1230 of stacked wafers. An array offabricated optical elements can also be called “wafer optics” as 1232and 1234 of FIG. 37. In wafer optics 1232 and 1234, each diamond 1233represents optics at the sensor level. An array of optics that acts ascorrectors can be called “wafer of corrective elements” as on a wafer1236 of FIG. 37. In wafer of corrective elements 1236, details are onthe pixel level and replication is on the sensor level. If thereplicated scale and spatial locations of all wafer optics matches thealignment of a CMOS wafer 1238 then the entire set of wafer optics andelectronics can be bonded together forming an array of imaging systems.In CMOS wafer 1238, each square 1239 represents one N×M pixel sensor.This array may be diced, thereby leading to a complete set of assembledoptics plus electronics. That is, wafers may be bonded together and thenthe stack is diced into individual sensors plus optics. In general thefunctions of imaging optics and corrective optics may be realized withone or more individual wafers. The particular designs of these elementsmay be optimized with that of the sensor pixels for increased lightcapture and sensitivity.

Returning briefly to FIGS. 31 and 32, details of correcting and steeringoptics, such as steering optics 920 and 958 of FIGS. 31 and 32,respectively, are discussed in further detail. The correcting andsteering optics may be designed with additional functionality thatprovide further advantages when used in combination with the imagingsystems described thus far.

The wafer of corrective optics 1236 and CMOS wafer 1238 of FIG. 37 canbe more fully described by FIG. 38. FIG. 38 illustrates a subsystem 2010including a combination of optics and electronics, in a cross sectionalview. Subsystem 2010 includes a CMOS wafer 2012 supporting a detectorarray thereon. Detector array 2014 includes a plurality of detectorpixels 2016 distributed across CMOS wafer 2012. Subsystem 2010 furtherincludes a lenslet array 2018 for increasing the light capture of thedetector array. Additionally, subsystem 2010 includes a ray correctionapparatus, generally indicated by a reference numeral 2020. Raycorrection apparatus 2020 is another example of wafer of correctiveelements 1236 of FIG. 37. In the embodiment shown in FIG. 38, raycorrection apparatus 2020 includes a transparent substrate 2022 with acorrective element 2024 attached thereto. Corrective element 2024 may beone optical element or a combination of a variety of optical elementsincluding, but not limited to, diffraction gratings, refractiveelements, holographic elements, Fresnel lenses and other diffractiveelements. Ray correction apparatus 2020 is configured such that incidentlight (indicated by an arrow 2030) may be received over a wide range ofincident angles θ_(in) and still reach one of plurality of detectorpixels 2016. That is, more of incident light 2030 would reach detectorpixel array 2014 regardless of incident angle θ_(in) with the presenceof ray correction apparatus 2020 than without. In essence, if the arrowindicating incident light 2030 is thought of as the chief ray ofincident light 2030, then ray correction apparatus 2020 substantiallycorrects for non-ideal angles of incidence of the chief ray such thatthe incident light would reach one of the plurality of detectors evenwhen incident from very far off of normal incidence. In this way,subsystem 2010 may accept input light over a fairly large cone ofincident angles and still function effectively. In the embodiment shownin FIG. 38, corrective element 2024 should be positioned close enough tolenslet array 2018 in order to minimize chromatic dispersion and pixelcross-talk.

For comparison, a prior art detector array subsystem without the raycorrection apparatus is shown in FIG. 39. FIG. 39 shows a crosssectional view of a portion of a detector array system 2035. As in FIG.38, incident light beam 2030, including a chief ray 2032, is incident ona portion of lenslet array 2018 at an incident angle θ_(in). Without thepresence of any ray correction in detector array system 2035, lensletarray 2018 focuses incident light beam 2030 at a spot in betweendetectors 2016 such that the incident light does not fall on a detectorand is consequently lost thereby reducing the sensed illumination.Common methods of increasing the detected light from large incident rayangle include shifting of the optical center of the lenslets 2018relative to the pixels 2016. While shifting the optical center of thelenslets improves performance somewhat, the improvement in possibleperformance is limited due to vignetting caused by the 3D nature ofcommon pixel structures. Therefore, subsystem 2010, including raycorrection apparatus 2020, as shown in FIG. 38 provides a significantimprovement in performance over prior art systems without the inclusionof a ray correction apparatus.

Turning now to FIGS. 40 and 41 in conjunction with FIG. 38, details ofthe effect of the presence of the corrective element in the detectorarray system are illustrated. First referring to FIG. 40, a subsystem2037 includes corrective element 2024 before the incoming lightencounters the lenslet array. Corrective element 2024 receives incidentlight beam 2030 at an incident angle θ_(in). Corrective element 2024 isconfigured so as to correct for the off-normal incidence such that,after passing through corrective element 2024, incident light beam 2030is then directed toward lenslet array 2018 at a near-normal angle suchthat the incident light beam is focused onto one of the detectors.

FIG. 41 shows a similar configuration including a corrective elementbut, unlike in FIG. 40, the corrective element is placed in the path ofthe incident light beam propagation after the lenslet array. As in FIG.39, the lenslet array in FIG. 41 begins to focus incident light beam2030 at a spot in between detector pixels 2016. However, correctiveelement 2024 in FIG. 41 serves to correct the direction of propagationof the resulting light beam such that the light beam then falls on oneof detectors 2016, thereby maximizing the detected illumination.

Turning to FIGS. 42 and 43, embellishments to the ray correctionapparatus in accordance with the present disclosure are shown. FIG. 42shows a detector system 2100 including a ray correction apparatus 2120including a plurality of corrective elements and transparent substrates.In the example shown in FIG. 42, ray correction apparatus 2120 includesa plurality of corrective elements 2122, 2124, 2126, 2128 and 2130.These corrective elements may be supported by a plurality of transparentsubstrates (such as transparent substrate 2022 supporting correctiveelements 2124 and 2122, and a transparent substrate 2132 supportingcorrective elements 2128 and 2130) or be independently positioned (suchas corrective elements 2124 and 2126. The stacking of a plurality ofcorrective elements yields further ray corrective effects than would bepossible with a single corrective element such that more compensationmay be effected for, for instance, large range of chief ray angles,wider range of wavelengths or higher diffraction efficiency. Detectors2016 may include, for example, monochromatic detectors and polychromaticdetectors.

FIG. 43 shows a configuration similar to detector system 2100 of FIG. 42but also includes a color filter array. A detector system 2200 of FIG.43 includes a combination of detector array 2014, lenslet array 2018, aray correction apparatus 2220 including a plurality of correctiveelements and transparent substrates in a stack configuration, as well asa color filter 2250 for color separation. The plurality of correctiveelements in ray correction apparatus 2220 may be configured such thatthe ray correction effected by the ray correction apparatus is tailoredfor a variety of wavelengths corresponding to the colors in the colorfilter. For example, ray correction apparatus 2200 may be configuredsuch that a green component of the incident light beam is directedspecifically through the detector/color filter combination configured todetect green light.

FIGS. 44-46 illustrate three examples of element forms that are suitablefor use as corrective elements in the ray correction apparatus of thepresent disclosure. FIG. 44 shows a refractive element 2302 forcorrecting the varying chief ray angle as a function of radialdimension. An example of such a refractive element is a field corrector.FIG. 45 shows a Fresnel lens 2304, with or without optical power, whichprovides an effect similar to that of refractive element 2302 butgenerally may be thinner than a refractive element along an opticalaxis. Fresnel lens 2304 is shown to include a ridged surface 2306 whichprovides the chief ray corrective effect. FIG. 46 shows a diffractiveelement 2310 including a surface 2312 with a spatially varying gratingperiod. Diffractive element 2310 may be configured, for example, tocorrect for arbitrary variations of the chief ray angle. As shown inFIGS. 42 and 43, a variety of corrective elements may be combined forgreater design flexibility.

Turning to FIG. 47, a top view of a detector system 2400 including anarray of corrective elements 2420 positioned over CMOS wafer 2012 isshown. As shown, for example, in FIG. 38, CMOS wafer 2012 includes aplurality of detector pixels 2016. Notice that the shape of the detectorpixels is not a simple square or a rectangular shape. In general theshape of the pixels can be quite complicated. The array of correctiveelements 2420 are placed over the plurality of detectors so as toprovide ray correction for light incident thereon. The shape and surfaceform of each of corrective elements 2420 may be tailored for the sizeand shape of the incident light beam and shape of the detector pixels.

FIGS. 48 and 49 illustrate the mechanism of ray correction by anexemplary corrective element. A corrective element 2502, as shown inFIG. 48, is a diffractive element for receiving a light 2504. Light 2504impinges on a top surface 2506 of corrective element 2502 at an incidentangle θ₁. When exiting from a ridged, bottom surface 2508 of correctiveelement 2502, light 2504 emerges at an output angle 02, which is lessthan the incident angle θ₁. Such a corrective element would be suitablefor use in the ray correction system of the present disclosure.

In a variation to corrective element 2502, a corrective element 2512 ofFIG. 49 includes a top surface 2514 with a reflection suppressioncoating 2516 deposited thereon. Reflection suppression coating 2516allows coupling of light from a large cone of angles away from thenormal such that the incident angle θ_(in) may be any angle less than90-degrees, depending on the specific coating design. Corrective element2512 further includes a bottom surface 2518, which in turn includes aplurality of alternating refractive surfaces 2520 and transitionalsurfaces 2522. The refractive surfaces are designed, possibly withcurved surfaces, so as to yield the desired ray correction to directlight 2504 at the appropriate output angle θ_(out). The transitionalsurfaces are sloped such that minimum light is scattered by thetransitional surfaces; for example, the transitional surfaces may bedesigned to be near the chief ray incident angle at that particular spoton the corrective element. The orientation of the refractive andtransitional surfaces may be tailored for a given type of light source,such as one including input optics that provide an incident cone oflight rather than a collimated light beam. The optical shape of therefractive surfaces can also be tailored for the particular imagingoptics being used.

Another aspect of correction elements, such as corrective element 2512of FIG. 49, is control of the chief ray as well as surrounding raysparticular to the imaging lens system and location on the sensor. Forinstance consider FIG. 50 as illustrative of this issue. In a system2600 shown in FIG. 50, corrective element 2024 acts to steer chief ray2032 such that, after the chief ray travels through lenslets 2018 andcolor filter 2250, chief ray 2032 is collected by pixel 2016 on wafer2012. FIG. 50 shows a chief ray perpendicular to corrective element 2024for ease of explanation. In general, the chief ray and other rays may beincident on corrective element 2024 at any angle. Rays 2632 are seen tobe far in angle from the chief ray 2032. Rays 2632 may be considered asthe edge rays from a general cone or rays loosely centered about thechief ray 2032. For fast imaging systems, the edge rays will be at alarge angle to the chief ray. For Wavefront Coded imaging systems, theedge rays may have uneven and even larger deviations from the chief ray.If corrective element 2024 is designed solely to steer chief ray 2032,then edge rays 2632 have a large chance of not being detected by sensor2016. This situation may be avoided by appropriate design of correctiveelement 2024 with knowledge of the imaging system between the object andthe sensor.

FIGS. 51 and 52 illustrate two representations of a specializedcorrector, an improved version of corrector 2512 of FIG. 50, thatcorrects the chef ray as well as surrounding rays through knowledge ofthe lens system. In contrast to FIG. 50, the edge rays 2632 of FIG. 51are corrected by corrector 2024, in addition to the chief ray 2032, suchthat the entire range of rays traverses the lenslets 2018 and colorfilter 2250 to be collected by pixel 2016 on wafer 2012. Corrector 2024corrects the chief ray 2032 and all other rays through knowledge of thelens system, or equivalently, the wavefronts generated by the lenssystem forming the image.

FIG. 52 shows a wavefront representation of the structure of FIG. 51.Wavefront 2652 is transmitted from the lens system (not shown) and ingeneral is dependent on the illumination wavelength and location on theimage. After corrector 2024 of FIG. 51, wavefront 2654 is substantiallyflat, compared to wavefront 2652. Wavefront 2654 only needs to be flatenough so that the illumination, after passing through the lenslets andcolor filters land within detector pixel 2016. Larger detector pixels2016, or less accurate lenslets 2018 require less flat wavefronts 2654.After lenslet 2018, wavefront 2656 is generated that is generallyconverging towards pixel 2016.

FIG. 53 shows the more general case of FIG. 51 through a wavefrontdescription and including a lens system 2100. In system 2700,illumination rays 2704 from object 2702 are collected by a lens system2710. Lens system 2710 includes a plurality of optics 2714. This lenssystem forms a chief ray 2032 and other rays 2732 that, along with allother rays, are represented by a wavefront 2752 for a particularillumination color and position on the image and/or location of object2702. Corrector 2554, like the corrector shown in FIG. 51, acts toremove much of the local wavefront tilt and produce a flatter wavefront2756 that is generally converging toward a particular detector pixel2016. Then, the rays from lens system 2710 are collected by pixel 2016on wafer 2012. The corrector uses knowledge of wavefront 2752, as afunction of illumination color and spatial position, to substantiallycancel the curvature of wavefront 2752 and produce a flatter wavefront2556 that allows a maximum of rays to strike the area of the detectorpixel. A focused image is not needed to be formed; what is important isthat the rays strike the detector pixel anywhere within the active area.Wavefront cancellation may be performed through, for example, but notlimited to, complementary surface shapes, volumetric variations of thecorrector, and holograms.

FIG. 54 shows another modification to the system of FIG. 51, this timewith the lenslets being incorporated into corrector 2024. In a system2800, a corrector 2810 now acts to substantially cancel the wavefrontfrom the lens system (not shown), and also chief ray 2030 and edge rays2632, such that, after color filter 2250, the wide variation of raysbefore corrective element 2810 are detectable at pixel 2016 on wafer2012. Corrector 2810 is shown as having a curved surface that repeatsover one or more pixels. The curved surface can represent the curvatureneeded to cancel the wavefront from the lens system as well as curvaturethat otherwise would be provided by the lenslets, as in FIG. 51. In thisway the corrector can be the only optical element between the lenssystem and wafer 2012. Alternatively, color filters 2250 may beintegrated onto or into corrector 2810 as well in a color imagingsystem. Although corrector 2810 is shown as having refractive surfaces,fresnel, and diffractive surfaces are equally suitable as are volumeholographic elements.

FIGS. 55-64 describe further methods of forming corrective elementsparticularly suitable for color imaging systems such as in FIG. 43.These corrective elements may be used alone or in conjunction with thetype of ray corrective elements of FIGS. 44 to 54 in a miniature camerasystem. A particularly important feature of corrective elements in FIGS.55-64 is color separation. Color separation is used so that differentcolors of light are spatially directed towards proper color filters, orpixel locations, so that light capture is greatly increased compared tonot using color separation.

Consider the use of color filter arrays used in imaging systems commontoday. Different pixels typically have different color filters, and amultitude of colors are then used with signal processing to form finalcolor images. A common color filter array pattern is called the Bayerpattern and consists of red, green, and blue color filters. The Bayerpattern is shown in FIG. 60. In prior art imaging systems all colors oflight that represent the object are incident at all relevant pixels. Ifa particular pixel and color filter location at the image coincides witha white color of the object then white light is incident on thisparticular pixel and color filter. If the color of this particular colorfilter is, for example, red, then only about ⅓ of the incident whitelight photons can be captured by this pixel, because the color filteracts to remove the blue and green photons. Corrective elements that areconstructed and arranged to provide color separation would spatiallyseparate the incident light so that mainly red photons are incident onthe red filtered pixels, mainly the green photons are incident on thegreen filtered pixels, and mainly blue photons are incident on the bluepixels. Any other type of color space, besides red, green, and blue, canalso be configured in this way so that certain proportions of red,green, and blue can be separated and directed towards certain pixels.Consequently, a greater share of the incident photons are capturedallowing higher signal strengths greatly increased low light imagingperformance.

FIGS. 55 and 56 show a conceptual drawing of a two level colorseparation subsystem in accordance with the present disclosure. Inpractice, a one level color separation system, rather than a two levelsystem, is sometimes necessary. The subsystem of FIGS. 55 and 56, in areplicated wafer configuration, is an example of the wafer of correctiveelements 1232 of FIG. 37. Illumination incident on the first correctiveelement (First Corrective Element 2855) is denoted as 2850. Thisillumination in general has red, green, and blue components inproportions dependent on the scene being imaged, the lens system, andthe spatial location on the sensor. The green component is representedin FIGS. 55 and 56 as two components, G1 and G2. G1 is a green red/greencolor, and G2 is a green, blue/green color. Illumination 2850 is shownas being perpendicular to first corrective element 2855 for ease ofillustration. After First Corrective Element 2855 and before SecondCorrective Element 2865, the R (red) and G1 illumination components areseparated from the G2 and B (blue) components into illumination 2860, asshown in the front view. The corresponding side view of FIG. 56 shows noseparation of illumination 2860 before second corrective element 2865,implying that a one-dimensional separation has been effected by FirstCorrective Element 2855. After Second Corrective Element 2865, the frontview in FIG. 55 shows no change in the color separation of illumination2870 (i.e., the illumination ray directions are unchanged by SecondCorrective Element 2865 in the front view). The side view of FIG. 56does though show additional color separation of the (R/G1) and (G2/B)components of illumination 2870. The color separation due to FirstCorrective Element 2855 is ninety degrees different from the colorseparation due to Second Corrective Element 2865. After both First andSecond Corrective Elements, the incident illumination 2850 has beenseparated into four spatially separate color components 2870. First andsecond corrective elements may be on opposite sides of a substrate, suchas in elements 2024 and 2122 in FIG. 43 with substrate 2022 in between.Furthermore, the two corrective elements that yield one dimensionalseparation can be combined into a single corrective element that yieldstwo dimensions of color separation. Corrective elements may be, forexample, substrates with modified surfaces or volume optical elements.

FIGS. 57-59 additionally illustrate the nature of color separation ofFIGS. 55 and 56. Initially, before the First Corrective Element,incident illumination 2850 is substantially, spatially uniform.Illumination 2850 ray bundle is described as fitting within a circularcontour, as shown in FIG. 57. After First Corrective Element 2855, butbefore Second Corrective Element 2865, illumination 2860 is now splitinto two regions 2862 and 2864 as shown in FIG. 58. The (R/G1)illumination components (region 2862) are spatially separated fromillumination components (G2/B) (region 2864). The ray bundles of theseillumination components are shown as smooth and overlapping. Benefitover the existing art may be achieved even if only the density of theillumination components are increased for a fraction of the illuminationcomponents. After First and Second Corrective Elements (2855 and 2865),illumination 2870 is further spatially separated in FIG. 59. The B, G2,G1, and B components have higher intensities in four spatially separatespatial regions (2872, 2874, 2876 and 2878). These regions are shown asnon-overlapping for clarity only—in practical devices, slight overlap ofthese regions are possible. That is, any high proportion of color inadjacent pixels corresponds to improved color separation. If the colorseparated regions correspond to individual detector pixels, such as 2016in FIG. 42, then each pixel in a 2×2 pixel region will sample photons ofa particular illumination spectrum. When the separated colors match theindividual detector pixel color filter then an increased amount ofillumination will be captured by the detector.

For instance, say the northwest pixel of a 2×2 region 2880 of FIG. 60has a red color filter. Then, if separated color of illumination 2880 inFIG. 61 is red at this location then this particular pixel will capturea larger fraction of incident photons than if the illumination where notcolor separated. This directly improves light capture and low lightimaging performance. If the spatial pattern of the separated color canbe distinct enough then the color filter array 2250 of FIG. 43 is nolonger required. The color separation with corrective optics alone canbe used to shape the spatial illumination spectrum in any desiredfashion. Instead of colors R, G1, G2, and B, the separated colors may beany desired mix. For example the three colors of magenta, yellow andcyan can be color separated and when used without R, G, and B colorfilters may produce a new color sampling of the image.

There are many methods which may be used to achieve color separationwith corrective elements. FIG. 62 shows one method of spatiallydispersing illumination by wavelength, a dispersive prism. The prismuses the dispersion of optical materials (i.e., change in refractiveindex as a function of illumination wavelength) in order to spatiallyseparate colors. Given the small nature of miniature cameras dispersiveprisms alone may not provide a practical solution for some systems.

In order to shrink the size and reduce the cost of corrective elementsthat have similar characteristics to dispersive prisms for colorseparation diffractive type of structures can be used as shown in FIGS.63 and 64, which illustrate compact methods of spatially dispersingillumination by wavelength. As is well known, diffractive structures arecommonly used to spatially separate illumination components ininstruments such as spectrometers. Even a simple two-level binarydiffractive structure as shown in FIG. 63 will diffract illuminationcomponents relative to their color. The angle the color component isdeviated directly depends on the wavelength. More complicateddiffractive structures can separate color components more efficiently bycontrolling the amount of light that is diffractive in unwanteddirections, or orders. These are often called blazed structures. Ablazed diffractive structure is shown in FIG. 64. These diffractivestructures could have more than two levels and have varying structureheights as a function of spatial position. The increasing sophisticatedstructures could more closely approximate the spatial color separationillustrated in FIG. 55 and FIG. 59.

FIGS. 65-70 describe the configuration of the exit pupil of an imagingsystem with Wavefront Coding to equalize the image SNR, or probabilityof detection for some systems, as a function of object distance. Manytask-based systems are used to acquire specialized information fromdistant objects. These task based imaging systems in general do not formideal images for a human eye. One example task-based system is abiometric imaging system, specifically an iris recognition system.Another example is an image tracking system. In both cases the distantobject is radiating or reflecting a certain amount of radiation. Theimaging systems in these example systems are configured to acquirespecialized information, such as an iris code or object (x, y) locationrespectively, in the presence of noise, imprecise optics and mechanics,etc. Ideally the information can be acquired with high precision andequally well over a large object volume. In some cases it maybedesirable to specify the precision or accuracy the information isacquired within the object volume. For example, information could bedeemed more critical depending on where in the volume the object islocated. The highest precision estimates of the information could bedesigned to correspond to the critical locations within the objectvolume. This is also useful in a general imager, say for instance whereimage quality from infinity to 1.5 meters is more important than say 1.5meters to 10 cm.

When imaging general scenes over a large object volume for human viewersit is often considered acceptable to configure the imaging system, orthe Wavefront Coded system if the volume is large enough, so that thecharacteristics of the optics are constant over the object volume. Themodulation transfer function or point spread functions, for example, areoften configured to form essentially the same values over a broad objectvolume.

A one-dimensional cubic phase imaging system plus ideal lens canillustrate this concept. For this system the phase profile added to theideal lens, or exit pupil, is p(y)=αy^3 for some constant α. Theparameter y denotes spatial location along the ideal one dimensionallens. We can consider the changing phase profile across the aperture ofthe lens as a continuously variable focal length change over the ideallens. As the focal length a lens can be approximated by the secondderivative of the lens phase, the change in focal length across a cubicphase system can be described as:Focal_length(y)˜d^2p(y)/d^2=6*α*x=β*xOr, the change in focal length across the lens is linear. We can thinkof a simple cubic phase system as an infinite collection of small lensesadded to the ideal lens with the focal length of the small lenseslinearly changing focal length across the aperture. This linear changein focal length results in an approximate constant MTF over some broadobject distance. Use of the Ambiguity Function allows simple analysis ofthese systems to show that the MTF is essentially constant over a broadrange of object distance or equivalent range of misfocus.

Consider the effect of a constant MTF at a particular spatial frequencyin a specialized detection system. Image information, as Shannon taught,is ultimately related to signal-to-noise ratio (SNR). Increasing the SNRincreases the maximum amount of information that can be extracted. Theresponse at a given spatial frequency for, say an image detectionsystem, is then the product of the object spectrum (magnified by theimaging system) and the MTF of the imaging system at this spatialfrequency. The noise is related to the amount of detector read noise,fixed pattern noise, and signal dependent noise (including shot noise)as well as other types of noise. As the object distance from theaperture increases less photons are captured by the entrance pupil ofthe imaging system. As the object distance from the aperture decreasesmore photons are captured by the entrance pupil. In an ideal system thetotal number of captured photons can follow an inverse square law withdistance. If the object response is then fundamentally changing withdistance, assuming for the moment a constant magnification with distanceor distant objects small enough to be considered points, then thesampled signal times the optical response, and hence SNR, for a givenspatial frequency will then vary even with a constant optical response.Even with a constant MTF, the overall object SNR and therefore imageinformation will be a function of object distance. When the imagingmagnification changes with distance, as it does in most systems, themagnification change further changes the SNR at one spatial frequencyover misfocus.

For numerous systems the image information should be constant, orspecifically controlled, as a function of object distance. We canacquire such a characteristic by changing the fundamental response ofthe MTF as a function of object location, or misfocus. As the totalamount of MTF values squared over all misfocus is a constant, by theConservation of Ambiguity property of optics, the MTF response can bepartitioned to form a constant or specified SNR system as a function ofdistance. Consider the plot shown in FIG. 65. This plot shows twoexample focal length vs pupil location curves for two differentWavefront Coded systems. The linearly changing focal length curverepresents a cubic phase system. The exponentially changing focal lengthcurve represents a new system designed to achieve a constant SNR overobject distance. The form of the exponential focal length change overthe aperture is focal_length(y)={α[b*(y)^2+c*y+d]}. In this particularexample b=c=12 and d=−4.

An Ambiguity Function (AF) representation for the linearly changingfocal length, or cubic phase system, is shown in FIGS. 66 and 67. FIG.66 shows the AF for the one-dimensional linearly changing focal lengthsystem. Radial slices through the origin of the AF represent the MTF asa function of misfocus. The misfocus aberration coefficient is linearlyrelated to the angle of the radial line. A horizontal slice through theorigin of the AF represents the in-focus (misfocus of zero) MTF. Avertical slice through the AF represents the value of the MTF at onespatial frequency as a function of misfocus.

Consider a vertical slice through the AF at normalized spatial frequency(or u-axis value) of 0.175. This represents the MTF at a normalizedspatial frequency of 0.175 as a function of misfocus. This verticalslice through the AF is shown in FIG. 67. Within the normalized misfocusregion of approximately +/− 0.2 the MTF at this spatial frequency isapproximately constant. Alternatively, a linearly changing focal lengthsystem results in MTFs that are essentially constant over an extendedmisfocus range. It is notable that, in FIG. 67, the response for onespatial frequency as a function of misfocus is substantially constantover the designed range.

FIGS. 68 and 69 show the AF for the exponentially changing focal length(photon compensating) system. The exponentially changing focal lengthsystem was shown in FIG. 65. The AF shown as the image in FIG. 68 isseen to be somewhat different from the AF shown in FIG. 66. The phasefunction has the form p(y)=α*(y^4+2y^3−2y^2). A slice through the AF at0.175 normalized spatial frequency is shown in FIG. 69. This MTFresponse as a function of misfocus is approximately linear when plottedon a log scale. On a linear scale then the MTF response as a function ofmisfocus is then approximately exponential. In FIG. 69, it may be seenthat the response for one spatial frequency as a function of misfocus issubstantially linear in a log scale (or exponential on a linear scale)over the designed range.

FIGS. 70 and 71 show the AF for an ideal traditional, ordiffraction-limited, imaging system without Wavefront Coding. The AFshown in FIG. 70 is seen to be very closely aligned with the horizontalaxis compared to the AFs from the Wavefront Coded systems of FIGS. 66and 68. This characteristic of the AF in FIG. 70 implies that the MTFsof the system without Wavefront Coding changes greatly with misfocus. Aslice through the AF at 0.175 normalized spatial frequency is shown inFIG. 71. This MTF is seen to be very narrow; there is a high MTF valueat zero misfocus but very small MTFs for normalized misfocus valuesslightly changed from zero. The SNR of an imaging system with this typeof MTFs is maximized at zero misfocus and minimized everywhere else.Notice that the response for one spatial frequency as a function ofmisfocus is large with no misfocus but very small everywhere else.

Due to conservation of ambiguity, the sum squared of AF values along anyparticular vertical line is a constant for any phase applied to the exitpupil of an ideal imaging system. Or the sum of squared MTF values atone spatial frequency for all values of misfocus is a constant. MTFvalues are therefore conserved. While the MTF values vs. misfocus forthe linearly changing focal length system are about 0.05 over themisfocus range of +/−0.2, the MTF values for the exponentially changingsystem vary from 0.03 to over 0.1. Increasing MTF values for some valuesof misfocus necessarily mean a decrease of MTF values for some othervalues of misfocus due to the conservation of ambiguity property.

But, the product of the object response vs. distance and the opticalsystem response of FIG. 69 can be matched with the exponentiallychanging focal length system to ensure a constant SNR and thereforeimage information as a function of object distance. The SNR and imageinformation for the linearly changing focal length system would changeas a function of object distance. SNR for the system without WavefrontCoding would be maximized at best focus and minimized everywhere else.If particular proportions of MTF values are required as a function ofobject distance, then a construction similar to that of those plotted inFIGS. 66-69 may be used to construct an approximation to the focallength varying function and then the resulting pupil function. Furtherrefinement through optimization would be required to fine tune theresulting pupil function. The MTF as a function of misfocus, orequivalently object range, can then be customized to suit the needs ofthe particular application. FIG. 72 is a flowchart illustrating a method3500 for applying Wavefront Coding to optical systems. The steps leadingto the design of a particular GRIN lens (e.g., any of modified GRINlenses 134, 802, 904 and 954) with wavefront coding to controlfocus-like effects are illustrated in method 3500. A general descriptionof this process follows.

Step 3510 is selection of a starting optical configuration. The opticalconfiguration includes the type and form of each element that acts tomanipulate light from the object to photon sensing elements or adetector array. The optical configuration includes a number of opticalcomponents in the system (for example, a three lens system) as well asthe type of components, such as refractive lenses, ray correctors,mirrors, diffractive elements, volume holograms, etc. Also, theparticular materials being used are determined, such as glass, plastic,particular glasses or plastics, GRIN materials, etc.

Step 3520 is selection of system parameters that can vary, or are notfixed in advance. These parameters will become part of an optimizationprocess (e.g., optimization loop 3540 below). System parameters caninclude the set of optical or mechanical materials that can be used,physical sizes and shapes of components and related distances. Overallfeatures such as weight, cost and performance can also be identified asparameters to be manipulated during optimization. Signal processing usedto form the final image also has parameters, such as silicon arearequired in an ASIC implementation to produce the final image, linearkernel values, dynamic range of filter kernels, non-linearnoise-reduction parameters, etc. Important parameters relevant towavefront coding include a form and type of aspheric opticalmanipulations to be applied to the imaging system. These parameters maybe fairly simple (such as surface height of a rectangularly separablesurface), or may be fairly complicated parameters that define, forexample, three dimensional indices of refraction of a volume imagingelement. A GRIN lens is one example of a volume imaging element. Avolume hologram is another example of a volume imaging element.

An initial optical design step 3530 includes traditional optics designas practiced in numerous textbooks where the design process isparticularly concerned with aberration balancing of non-focus relatedaberrations. Optical design step 3530 may be eliminated in certain cases(for example, when off-the-shelf optical components provide initialassumptions for the optical design). Focus-related aberrations includeaberrations such as spherical aberration, field curvature, astigmatism,chromatic aberration, temperature related aberrations, and fabricationand alignment related aberrations. Non-focus related aberrations includeaberrations such as coma, lateral chromatic aberration and distortionthat cannot implicitly be corrected by movement or warping of the imageplane as a function of variables such as field angle, color, temperatureand alignment, if such warping was in some way possible. Optical designstep 3530 concentrates on removing effects of aberrations that cannoteasily be removed with specialized optics design and signal processingof the final imagery. Focus-related aberrations can be removed withspecialized optics and signal processing. Optical design step 3530includes providing an initial guess with regard to the parameter set ofthe optical system.

With an initial optical design, the joint optimization of the opticaland digital components can begin. An optimization loop 3540 modifiesoptical design parameters specified in step 3520 until some final designcriteria are met. Optimization loop includes steps 3550, 3560, 3570,3580 and 3590, as discussed below.

In a modifying step 3550, the initial guess of parameters is applied tothe initial optical design from step 3530, forming a modified opticalsystem.

Step 3560 determines signal processing parameters that will act on aformed image to produce a final image. The signal processing parameterscan include, for example, the size and form of a two-dimensional linearfiltering kernel. The signal processing parameters may be selected basedon the particular modified optical system of step 3550.

After the signal processing parameters have been determined in step3560, corresponding signal processing is applied in step 3570 tosimulated imagery from the modified optical system. The simulatedimagery can include images of specialized targets such as points, lines,grids, bars, etc. and/or can be color images of general scenes.Simulated images can include noise from models of actual or idealdetectors, such as shot noise, fixed pattern noise, read noise, etc.

Step 3580 evaluates simulated optical images and signal processing fromstep 3570 to determine whether overall system specifications are met.The specifications can include imaging performance, such as particulardefinitions of image quality as a function of field position, color,object scene, light level, etc., and can also include system dimensions,optical element sizes, optics, electronics and system costs, tolerancesto fabrication, assembly and temperature, for example. Metrics may becalculated from the simulated imagery, and the metrics may benumerically evaluated to see if they fall above or below target values.The metrics and target values may act to translate image quality as seenby a human into numeric values recognizable to a computer. Task-basedapplications (like, for example, iris recognition) may haveapplication-specific, numeric metrics that can remove the need totranslate a parameter of image quality to a numeric value. If step 3580determines that the modified imaging system meets the specifications,then the design process is done. If step 3580 determines that themodified imaging system does not meet the specifications, furtheroptimization of parameters is performed in step 3590. Duringoptimization, parameters of the optical system are changed in order todirect the system toward a particular system that meets the systemspecifications. The method of changing of the system parameters duringoptimization is a general problem with many types of solutions. Typicalmethods of changing or optimizing parameters may involve a trade-offbetween speed of optimization and ability to find global maxima orminima. Linear search methods such Gradient Descent are useful, as arenon-linear methods such as Nelder-Mead or Genetic Search. Selection ofthe optimization method may be a function of the complexity of theparticular imaging system being designed.

After system parameters are changed in step 3590, optimization loop 3540repeats: the new parameters are then used to modify the optical systemin step 3550, the parameters of the signal processing are determined instep 3560, imagery before and after signal processing is formed in step3570, and so on. Eventually optimization loop 3540 terminates by step3580 finding that the specifications are met, or through no convergencewith no suitable solution being found.

An example of method 3500 is the design of the modified GRIN lens 134 ofFIG. 11. The method began with the selection of an off-the-shelf GRINlens. An NSG ILH-0.25 GRIN lens, and a grayscale detector having 3.3micron square pixels, were selected in step 3510. Ideal pixels, no raycorrector, and simple linear signal processing were selected in step3520. Also in step 3520, aspheric modifications placed at the frontsurface of the GRIN lens, that is, modifications to front surface 135 ofGRIN lens 134 of FIG. 11, were chosen to be rectangularly separablecubic forms. The surface form of a rectangularly separable cubic wasdefined as height(x, y)=α(x.^3+y^3). Only one optical parameter, α,corresponding to a maximum surface deviation, was determined in thisexample.

As only a modification of an off-the-shelf GRIN lens was being designed,step 3530 was omitted in this example. By way of contrast, if acustom-designed GRIN lens, with no modification to its front surface hadbeen the goal, then step 3530 would have been needed.

A particular first value for the cubic surface deviation parameter a wasarbitrarily chosen as α=0. A rectangularly separable cubic phasemodification with parameter a was made to the lens via custom simulationtools in step 3550.

Signal processing parameters were calculated in step 3560 and applied instep 3570 for this particular modified GRIN lens, such that the formedimagery had high MTF values and compact PSFs. As linear filtering wasused, a calculation used to determine the linear filter was:Final_PSF=Sampled_PSF*Linear_Filterin a least squares sense, where the symbol * denotes two-dimensionallinear convolution. A Sampled_PSF value is determined in step 3560 fromthe modified GRIN lens simulations and digital detector. The Final_PSFwas selected in step 3560 as a PSF generated from a traditional opticalsystem that had the majority of power concentrated in one pixel. The MTFcorresponding to this particular final PSF had a value (at the highestspatial frequency of the detector) of about 0.4. Those skilled in theart of signal processing can appreciate that numerous methods can beused to solve these least squares linear equations to determine thelinear filter based on the sampled PSF set and final or desired PSFs.The calculations can of course be done in the frequency domain, and/oriteratively.

With the digital filter calculated, the PSFs and MTFs after signalprocessing were produced in step 3570. These PSFs and MTFs after signalprocessing were then. compared in step 3580 to visual image qualitymetrics that translated to the majority of PSF power being in one pixelover all image fields, and the corresponding MTFs having minimum valuesabove 0.3 after signal processing. In the first iteration ofoptimization loop 3540, neither the PSFs nor MTFs after signalprocessing with α=0 met the system specifications. A Nelder-Meadoptimization was then begun in step 3590 to determine a choice of theoptical parameter a, and the linear filter, to improve the opticalsystem. The final solution of the optimized optical parameters is shownin FIG. 18. The peak-to-valley optical path difference is about 11wavelengths (or α, in optical path difference space, of approximately 11λ). A corresponding linear filter of the signal processing wascalculated to transform the sampled PSFs of FIGS. 19, 20 and 21 to thePSFs of FIGS. 22, 23 and 24. The PSFs of FIGS. 22, 23 and 24 arevisually seen to have the majority of the power in one pixel, ascompared to the PSFs of FIGS. 19, 20 and 21. The corresponding MTFsafter signal processing 170 of FIG. 25 are all seen to be above 0.3. Themaximum spatial frequency of the detector is 151 lp/mm. The actual formof the linear filter is seen in FIG. 26 and FIG. 27. This particularlinear filter can be thought of as being similar to an inverse filter ofthe essentially constant sampled PSFs of FIGS. 19, 20, and 21.

Changes may be made in the above methods and systems without departingfrom the scope hereof. It should thus be noted that the matter containedin the above description or shown in the accompanying drawings should beinterpreted as illustrative and not in a limiting sense. The followingclaims are intended to cover all generic and specific features describedherein, as well as all statements of the scope of the present method andsystem, which, as a matter of language, might be said to fall therebetween.

Although each of the aforedescribed embodiments have been illustratedwith various components having particular respective orientations, itshould be understood that the system as described in the presentdisclosure may take on a variety of specific configurations with thevarious components being located in a variety of positions and mutualorientations and still remain within the spirit and scope of the presentdisclosure. Furthermore, suitable equivalents may be used in place of orin addition to the various components, the function and use of suchsubstitute or additional components being held to be familiar to thoseskilled in the art and are therefore regarded as falling within thescope of the present disclosure. For example, although each of theaforedescribed embodiments have been discussed mainly for the case ofchief ray correction, one or more corrective elements may be combined toprovide illumination correction for beam width differences arising fromvariations in beam angle. An angled, refractive surface, for instance,would be suitable for such an application, and may be further combinedwith, for example, a diffractive pattern in order to simultaneouslycorrect for chief ray angle.

Therefore, the present examples are to be considered as illustrative andnot restrictive, and the present disclosure is not to be limited to thedetails given herein but may be modified within the scope of theappended claims.

What is claimed is:
 1. An imaging system, comprising: a plurality ofdetectors forming a detector array, an optical component comprisingaspheric optical structure such that an optical modulation transferfunction (MTF) of the imaging system has no zeroes in a passband of thedetector array, a ray corrector positioned between the optical componentand the detector array, wherein the ray corrector directs incident raysonto at least one detector of the detector array with an angle ofincidence that is closer to a surface normal of the detector array ascompared to an angle of incident rays on the detector array without theray corrector.
 2. The imaging system of claim 1, the optical componentcomprising a lenslet array.
 3. The imaging system of claim 1, whereinthe ray corrector comprises a gradient index (GRIN) lens.
 4. The imagingsystem of claim 3, further comprising a correction plate positionedbetween the GRIN lens and the detector array.
 5. The imaging system ofclaim 1, wherein an array of gradient index (GRIN) lenses formed as astack forms the ray corrector.
 6. The imaging system of claim 1, furthercomprising a post processor connected with the detector array forcompensating effects of the aspheric optical structure.
 7. The imagingsystem of claim 1, further comprising a color filter array to filtercolor for the detector array.
 8. The imaging system of claim 1, the raycorrector comprising one or more of a refractive lens, a Fresnel lensand a diffractive element.
 9. The imaging system of claim 1, wherein theray corrector comprises an array of ray correctors formed as a stack.10. The imaging system of claim 9, each of the ray correctors configuredto redirect light of a particular color to at least one detector of thedetector array.
 11. The imaging system of claim 9, each of the raycorrectors being configured to redirect light into a respective detectorthat is non-rectangular.
 12. An imaging system, comprising: opticalcomponents that form a plurality of optical channels; and a detectorarray; each of the optical channels including (a) portions of theoptical components that steer incident light into at least one detectorof the array and (b) an aspheric gradient index (GRIN) lens.
 13. Theimaging system of claim 12, an aspheric surface of the aspheric GRINlens imparting a phase modification to implement wavefront coding. 14.The imaging system of claim 12, wherein a modulation transfer functionof each of the optical channels has no zeros within a passband of thedetector array.
 15. The imaging system of claim 12, further comprising asignal processor to provide a final image based upon phase effectsinduced by the aspheric GRIN lens of each of the channels.
 16. Animaging system, comprising: a block of optically transmissive materialhaving an entrance aperture, an exit aperture and at least oneinternally reflective surface, wherein a wavefront transmitted throughthe entrance aperture reflects off of the reflective surface and exitsthe exit aperture with a phase modification to implement wavefrontcoding.
 17. The imaging system of claim 16, wherein an external surfaceof the block imparts the phase modification and comprises one of theentrance aperture and exit aperture.
 18. The imaging system of claim 16,wherein the reflective surface is aspheric to impart the phasemodification.
 19. The imaging system of claim 16, wherein the exitaperture comprises a flat section of the block, for mounting onto afocal plane array.
 20. An imaging system, comprising: a plurality ofoptical channels and a detector array, each of the optical channelsassociated with at least one detector of the array and having anaspheric ray corrector, wherein the aspheric ray correctorpreferentially directs color towards particular detectors of thedetector array.
 21. A photon compensating optical system, comprising: atleast one optical element and an aspheric surface, wherein anon-constant modulation transfer function (MTF) of the systemcompensates for a range between an object and the optical element. 22.The photon compensating optical system of claim 21, wherein the asphericsurface comprises a surface of the optical element.
 23. The photoncompensating optical system of claim 21, the aspheric surface having anonlinear focal length change across its aperture.
 24. The photoncompensating optical system of claim 21, the aspheric surface having anonlinear focal length change across its exit pupil.
 25. The photoncompensating optical system of claim 21, wherein the optical system hasa normalizing energy distribution across a focal plane over the range.26. A ray corrector, comprising: an optical element configured forplacement adjacent to, or coupling to, a detector array, the opticalelement forming at least one surface such that field rays within anoptical imaging system are directed towards the detector array with anangle of incidence that is closer to a surface normal of the detectorarray as compared to angle of incidence of field rays incident on thedetector array without the optical element, wherein the at least onesurface comprises aspheric optical structure such that an opticalmodulation transfer function (MTF) of the imaging system has no zeroesin a passband of the detector array.
 27. The ray corrector of claim 26,wherein the optical element comprises one of a gradient index (GRIN)lens, a refractive lens, a Fresnel lens and diffractive lens.
 28. Animaging system, comprising: a first wafer comprising a plurality ofdetectors; and a second wafer including a plurality of aspheric opticalcomponents such that an optical modulation transfer function (MTF) ofthe imaging system has no zeros within a passband of the plurality ofdetectors; the first and second wafers being stacked to form the imagingsystem with a plurality of optical channels, each of the opticalchannels having at least one optical component and at least onedetector.
 29. The imaging system of claim 28, further comprising a thirdwafer stacked with the first and second wafer, to provide opticalspacing for the imaging system.
 30. The imaging system of claim 28, theoptical components comprising a lenslet array.
 31. The imaging system ofclaim 28, further comprising a third wafer stacked with the first andsecond wafer and an array of ray correctors, each of the array of raycorrectors being configured to direct incident rays onto at least oneassociated detector with an angle of incidence that is closer to asurface normal of the detector array as compared to an angle of incidentrays on the detector array without the array of ray correctors.
 32. Theimaging system of claim 31, wherein the aspheric optical componentscomprise a lenslet array.